König, Heinz

On the inner Daniell-Stone and Riesz representation theorems

Doc. Math., J. DMV 5, 301-315 (2000)


Summary: The paper deals with the context of the inner Daniell-Stone and Riesz representation theorems, which arose within the new development in measure and integration in the book 1997 and subsequent work of the author. The theorems extend the traditional ones, in case of the Riesz theorem to arbitrary Hausdorff topological spaces. The extension enforces that the assertions attain different forms. The present paper wants to exhibit special situations in which the theorems retain their familiar appearance.

Mathematics Subject Classification

28A12, 28A25, 28C05, 28C15


inner extensions, inner premeasures, Radon measures, Radon premeasures, positive (=isotone) linear functionals, inner sources, inner preintegrals, Radon preintegrals, tightness, theorem of kisyński